Method of generating gears



Dec. 7 ,1926.

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N. TRBOJEVICH I METHOD OF GENERATING GEARS Filed June 25 1923 6 Sheets-Sheet 6 GEM/e130 improved hob of the Patented Dec. 7, 12326,

UNITED sra'r'ss NIKOLA. TRBOJEVICH, 015 DETROIT, MICHIGAN.

METHOD or GENERATING GEARS.

Application filed June 25, 1923. Serial No. 647,670.

The invention relates to a novel method of gear generating which is applicable to milling or grinding of spur gears having either straight or helical teeth. In partic-' ular,

this method is a combination of the well known hobbing and the fiy-tool methods, and unites the advantages 'of both methods to such an extent that it is capable of producing gears having accurate and smoothly finished tooth surfaces, in a continuous and rapid cutting operation.

The elements which make up this method are a novel hob or milling cutter, a novel grinding wheel a novel generating machine and a novel wheel truing device, all of which are also inventions of mine. "However, this application deals with the method of generating only. In the drawings Figures 1 to and Figure 21 are'diagrams explaining the mathematical principles involved;

' Figure 11 is a side view of my, improved hob; i

Figure 12 view; t I

Figure 13 is a fragmentary view of my milled tooth type. J Figure 14 is a meridian section of my shows the same hob in plan improved helicoidal-grinding wheel;

Figures 15 to 17 illustrate my novel meth- 0d of wheel dressing;

Figure 18 is the front elevation of a typical generating machine adapted to grinding of spur gears according to my method; Figure 19 is the side elevation of the machine; r

Figure20 is the plan view thereof; Figure 22 illustrates a method for simul taneously generating the opposite sides of the gear teeth.

In order to understand this new process of gear cutting, it is necessary first briefly to refer to the mathematical principles upon which the process is founded. It is known that an involute gear is defined by the fact that it correctly meshes with a rack having equi-spaced -teeth composed of plane segments only. It may be stated broadly that all involute surfaces may be generated by a rolling-0E process, from a plane. .clherefore, in all gear generating processes now used, the iinaginaryrack plane forms an indispensable factor, either by its particular form, or by its move- I steps:

blank 7 (Figure 3),

and the cutting, tool,

ment, describes in some gearis developed. Thus, the generation of a gear may be theoretically divided into two first, the reproduction of the rack plane by the cutting edges of the tool and second, the rolling off process or the developing of tooth surfaces from said Plane or planes.

In Figures 1 and 1, the principle of the ordinary hobbing process is shown. -The gear blank A meshes with a rotating worm B having a length greater than where Dis the depth of tooth and ,c is the angle of pressure. It will be seen that the ordinary hob is equivalent to a rack of an infinite length and an infinitesimal width. In order to generate a blank A having a width 7 it is necessary that the imaginary rack should have the width 7, at least. For this reason the hob must be translated along the axis of theblankf It is interesting to note-that if the hob were of an infinite diameter it would notbe necessary to have a special longitudinal feed movement. 1 In that case agear blank might be correctly generated by the intermeshing action alone of the hob and the blank.

Figure 2 shows another principle of generating, which is different from hobbing. A conical fly tool F having a plane cutting face d is inclined with respect to the tangent plane of the blank to an angle B, and is manner the imag- .inary rack plane from which the particular translated tangentially as indicated by the arrow while the blank rotates in unison, that is, has a pitch line velocity equal to the velocity of translation of the cutter, v

The diameter of the cutter F is comparatively large with respect to the width of the so that it may finish the tooth surfaces 6, b 6 etc., one in each stroke (Figure 3). Evidently, so far as the generatlon of the gear A having the coinparatively narrow width f is concerned, the tool F is equivalent to a rack of infinitesimal length, but of an infinite width. Thus, in this method, the' longitudinal feed is not necessary. However, it is necessary to reciprocate the tool tangentially, and to index the-blank between the strokes in order to expose the surfaces b, 6,, 6 etc. successively to the generating action of the tool. Furthermore, in order to generate the opposite curves 0, c 0 etc. the blank must be reversed on its arbor and the process repeated.

The fly tool method as shown in Figures 2 and 3, is extensively used in gear grinding. Its advantages are that it finishes the Whole face of the tooth in one out, without the .longitudinal feed, and therefore, produces a good finish. Also the cutting face (Z being a plane, is comparatively easy to accurately reproduce in the grinder. There is, however, a drawback inherent to this method and that is the need of mechanical indexing between the strokes of the' tool.

Not only that a portion of the cutting time is thus non-productively spent in indexing, but the intermittent indexing operation also inevitably leads to more or less irregular spacing ofteeth, which latter is a serious defeet in a gear.

In my new method, a cutting tool of a novel form is used. Thecutting surface is a right helicoid 0, limited by two parallel and co-axial cones (Figure 5). It is well known from mathematics that the right helicoid is a mathematically unique surface, as

it approaches its tangent plane the most intimately of all twisted surfaces. In the language of mathematics, the surface is the only realminimal ruled surface, (Theorem of Catalan), and has the property that its generators (the radial lines and the helixes) first form an orthogonal system, and second, are the asymptotic lines of the surface. Therefore, the tangent plane T at any point Q, of the surface (Figure 6) which latter is defined by the particular helix zconst. and the particular radial line zconst. passing through'it, intersects and osculates the surface 6 along said two lines at right angles.

It is easily'proved that if a comparatively small segment having the length f and the radial width D is out out from a righthelicoid having a comparatively large radius R and a small lead of thread L, Figure 4 said segment may be considered for all practical purposes as a plane parallelgram, as the distances A2 and A2 separating the surface from its tangent plane T are extremely small. I have calculated that if a cutter of" only 10 inches diameter is used to cut 10 dia, metralpitch gears having a pressure angle [3:20 degrees and a width of face -1 inch, the maximum A2 (in the four corners) is less than 0.0001 while the same distance on the pitch line is less than 0.0((001.

Thus, it is seen that my invention consists I mainly in findinga new form of a hob having a tapering helix, and a right helicoidal cutting face, the radius of curvature of' which face may be considered as infinite for all practical purposes. Such a hob acts, then as a rack having doubly infinite di-' mensions, that is, it acts with a continuous intermeshing action, the same as the common hob, and yet it finishes the full width of the gear face in one cut, the same as the aforementioned conical fly tool. I have calculated that if the same effect was to be obtained'by the spur hob of the conventional design, as is obtainable by this novel hob of only'lO inches diameterlO pitch, the diameter of such a hob would have to be over feet.

The method of calculating the amount of discrepancy of the surface from its tangent plane (the rack plane) at any point is the,

following. The equation of the helicoid 6 (Figure 5) may be written down. and also the equation of its tangent plane at any.

point Q, (Figure 6 and Figure 10). A circular ring segment Pi, P P P having a width 7' (Figure 10) is cut outboth from the helicoid e and its tangent plane T. The difference between the corresponding 2 coordi' 'nates of the two surfaces will be always equal to, or greater than the actual distance between said surfaces and is indicative of the error in tooth curves at that particular point. i i The equation of the surface is where p and (p are the parameters (see Figure 5) while Z is the lead of the helix measured along theZ axis.

The equation of the tangent plane is ob tainable from (1) by forming first the partial derivatives of w, y, z, with respect to p and (p and by placing said values in the well .known determinant A=0. To simplify the calculation, we determine the tangent plane at the point'Q (R, O, O). Denoting the current coordinates with 5, 77, we have then as the equation of said tangent plane a where R is the pitch radius of the helicoid.

In order to obtain a formula which is silt-- ficiently close and yet simple, I have 'devel- T oped the equation (5) into an infinite series, and after'omitting the infinitesi nal s of Error on the outer corner:

where f is the width of face of the gear, It the pitch radius of the cutter in inches, [2 the cone angle or the angle of pressure, P the diamtral pitch. It is also assumed that the gear tooth has a standard addendum and dedendum Figures 79 show the relative positions of the helicoid with respect to the rack plane T on the pitch helix, on the root helix, and on the outside helix respectively, while from Figure 6, an idea may be had of the peculiar osculating Contact of the surface with said plane. In particular, the dotted line qshows the locus inside of which the error is everywhere less than a certain assumed A2.

From the above explanation the principle of operation will be understood. The conical hob G, Figure 4, acts in a doub.e capacity, first as a spur hob B, Figure 1, and

. second as a conical fly-tool F, Figure 2.

The hob G is rotated and tangentially translated as indicated by the arrows (Figure 4) while the blank A is also rotated to maintain the proper timed relation. In consequence, all the curves b, 1),, 6 etc. are simultaneously generated in a single passage of the tool, and furthermore, a blank having a considerable width of face f is fully generated over its entire face without the need of a longitudinal feed. The several advantages of this method are obvious; first there are no longitudinal feed marks on the tooth surfaces such as are found in the ordinary hobbed gears; second there are no flats on the tooth curves on account of the tangential feed which makes the hob appear as i it has an infinite number of gashes; third, the hob may be made quite narrow, and in my preferred construction it has always less than one full convolution of the helix compared with at least three full convolutions necessary in the ordinary hob which has no tangential feed. When the process is used for grinding, the advantages become even more important, as this is to my knowledge the first practicable process ever evolved for grinding gears in a continuous interme'shing generating operation. Owing to the fact that less than. one full convolution of the helix is sufficient to properly generate the tooth curves, the helicoidal face of the grinding wheel being readily accessible at every point, may be accurately trimmed by means of a diamond without any great difliculty, as it will be presently shown.

The method of generation consists of the following stepsz-A tapered hob is-first selected having a cone angle equal to the angle of pressure'to be generated, and a diameter and pitch selected with reference to the gear to be generated, Said hob is placed in such a position relatively to the blank that its cutting face (the segment P P P P Figure 10) coincides with the rack plane segment T from which the gear is developed.

'It will be understood that in this manner both straight and helical teeth may be gen erated as required. Third, the hob and the blank are rotated in a timed relation and a relative movement of translation is imparted to the hob in a direction. perpendicular to the face of the blank. In such a manner the sides of teeth 6, 6 3), etc. (Figure 4) facing the generator g are fully generated. The opposite sides 0, c 0,, etc. may be generated either by employing another cutter inclined in the opposite direction or by reversing the blank on its arbor and repeating the process.

Figure 22 illustrates a method for simultaneously generating the contour of the gear teeth upon opposite sides thereof. The two cutters or grinders 73 and 74: are arranged so that their respective cutting faces 75 and 76 coincide with opposite sidesof the rack element T, sufficient clearance between the cutters being provided by allowing one or more intervening rack tooth spaces. The grinder 73 is provided with a right hand and the grinder 74 is provided with a left hand helix, one being rotated oppositely of f vided for tilting or swiveling the cutter about an axis perpendicular to the common tangent plane, in order to bring the cutting helicoid in complete tangency with respect to the imaginary rack plane T. Having thus described my method proper, I shall also briefly describe its novel e ements. namely. the hob, the grinder, the generating machine and the wheel dressing device.

The hob.

Figure 11 and Figure 12 are two projections of mv improved tapered hob of'the backed-off type while Figure 13 shows a fragment of hob of the milled tooth type. The cutting helicoid e is first turned or milled in the truncated cone blank G, after in the preferred type.

which a number of equi-spaced gashes or flutes i are milled across the helical thread, and the remaining teeth are relieved by a movement of the relieving tooth perpendicularly to the side of the cone. It will be seen that such a hob may be also ground after hardening all over, and in that mannor a cutting tool of an utmost precision is obtained. It is also possible to repeatedly sharpen the hob in the faces i Without changing its correct tooth form.

The milled tooth type hob shown in Figure 13 is similar to the hob above mentioned in'every respect, except that in the latter case the teeth are sharpened along the lands h and not in the gashes as is done The grinding wheel. The grinding wheel is similar in every respect to the hob shown in Figures 1112,

except that it usually has a much larger di ameter, is made of abrasive material and has no gashes or teeth as has the steel hob. A grinder of this kind is first turned in a lathe to an approximate shape (see Figure 14) balanced both statically and dynamically, after which its cutting helicoidal face e is trued up by means of a trimmer diamond. Figure 14 shows a suitable cross section that might be given to such a wheel in order that it may be repeatedly trimmed without losing its form. The successive trimmed surfaces are the helicoids 6, e e etc. and the cones m, m m etc.

' The wheel dressing device.

' irregular cutting contour by rotating the Y vwheel only slowly, by mounting the trimmethod less than one full convolution of the 'ming diamond eccentrically on a spindle running at a high rate of speed, and by giving the trimming spindle a movement of translation relatively to the wheel and in a timed relation with respect to the rotation of said wheel. I consider this discovery as being of great practical importance as it enables me to employ the hobbing principle for grinding of gears. It has been repeatedly suggested in the art prior to my invention, that gears should be ground on the hobbing principle, but no one has yet produced means for accurately and quickly dressing the wheel to the required helicoidal shape. Now it is possible to accomplish that, and my tapered hob method is particularly suitable for that purpose because in that helix is suflicient to properly generate the involute tooth curves.

Figures 15-17 show the new principle of dressing abrasive helicoidal surfaces. The diamond 21 is mounted 011a rotary spindle 22 and driven either by a pulley 23 orby a small electric motor not shown).' The movement of the grinder G is entirely independent of the rotation of the trimmer 21 on its axis. Grinder G is mounted on the auxiliary spindle 24, one end of which is formed into an accurate master screw 25 engaging the fixed nut 26 and having the exact lead of helix as is desired in the grinder, while the other end of the spindle 24 is formed into a smooth journal 27 housed in the bearing 28 and longitudinally movable in the same. A large spur gear 29 is keyed to the spindle 24 and may be operated by means of the long inion 30 and the handwheel 31. It will e understood that when the handwheel 31 is rotated the grinder G, will describe a helical path, and its cutting surface e will be properly trimmed by the diamond 21 rotating in a stationary plane. Figure 16 shows that when the trimmer=-21 rotates about the axis 22 it described- 32, while that wheel trims the softer mainwheel G The object of this arrangement is to shorten the time required for dressing of the main wheel, and also to save the diamond from excessive wear.

The generating machine.

A machine embodying my invention and adapted to grinding of spur gears is shown in three views in Figures 18-20. The general organization of such a machine is not broadly new, as there were in use prior to my invention hobbing machines operating on the principle of tangential feed. Such hobberswere mainly used for hobbing of worm gears by means of a fly-tool or a tapered hob.

Referring now to Figure 18, the grinder G is securely mounted on the end of the spindle 33 which is housed in suitable bearings 34 and 35 and is driven by means of the pulley 36. The mounding of the grinder head on the vertical column 37 is such that the wheel may be raised or lowered and also clamped in any intermediate position. The vertical adjustment is necessary in order to permit of using grinders of various diamis mounted upon the end of the spindle 33 furthest from the grinder. Said mitre meshes with the similar mitre 39 on the shaft'40, at the end of which shaft a universal joint 41 actuates the telescopic shaft 42, the second universal joint 43, the shaft tation of the cutter and the blank; andmay be operated either by hand or by power,

without disturbing flsaid timed relation. In

order to accomplish this, a differential mech anism is employed, said 'mechanism consisting of two screws and two slides connected with change gearing. I I

The work spindle 55 is housed in the work head 57 which is asubstantial casting and is slidably mountedon the top of the base 58. The handwheel 59 'ismounted on the end of the feed screw 60 which is housed in the bracket 61 and engages the nut 62 in I the work head 57.

The main drive worm 53 is made of a suflicient length and is housed in two bearings 63 and'64 integral with the differential slide 65. Said slide is mounted in the ways 66 of the base 58 and is actuated from the handwheel 59 through thedifierential change gears 67, 68,69 and 70, the screw 71 and the nut 72. The arrangement is such that when the workhead 57 carrying the worm gear 54 moves in a certam directlon, the difierential slide 65 carrying the worm 53 moves in the opposite direction. In such a manner a proper increment of rotation may be imparted to the blank to compensate for the feed movement.

The action of said differential may better be understood from the Figure 21'. In order to translate the gear blank 56 through a distance 8,, both the blank and the worm gear 54 must receive the increment ofrotation w where r yw zs zr w It will be understood that for a feed of S inches the worm 53 mustbe pulled'back a distance equal'to S n-S where s zr 'ur 'The wheel dressing device such as was shown in Figure 15,.or Figureil7 is prefer ably mounted on the generatin itself as a permanent fixture, athough it might prove practicable to dress th ing wheelin a separate machine. aid device has been omitted from the machine views Figure 18 to Figure 20, in order to make the drawings clearer. t

What I claim as my invention is 1. A; method for generating gears consisting in placing a right helicoidal tapering machine grindcutter having a conical pitch surface and a conical' helix forming in plane development an Archimedean spiral in relation to the work, such that the helicoid is tangent to the imaginary rack plane generator and in rotating said cutter and work in timed relation;

2. A. method of gear generating in which a right helicoidal tapered hob the helix of which forms in development an Archime .Qde'an spiral and the cone angle, diameter'and 1 pitch of which are selected with reference to the gear to be generated, is placed in a tangential relation with respect to the imaginary rack plane meshing with .said gear at about the middle of its face, in which'the.

cutter and the blank are rotated in a timed relation and the cutter is given a relativemovement of translation 111a. direction transverse to the axis of blank. .I

3. method of gear cutting consisting in rotatlng the. blank and a right helicoidal tapering cutter'the generating helix of which,

forms in plane development an Archimedean spiral in a timed relation in such amanner mtermeshmg are both tangent to a common rack plane, and in imparting 'a relative movement of translation to the cutter across such a manner that the gear teeth and the helicoid while intermeshing are always tangent to a common rack plane; and in imparting a relative movement of translation to the cutter in a direction perpendicularv to the axis of the blank.

5. A method for grinding gears which consists in placinga grinder having a conical helicoidal abrasive surface the pitch helix of which forms in plane development an Archimedean spiral in such relation to the gear to be ground that said surface'is tangent to the imaginary rack plane generator andin rotating said gear and grinder in timed relation.

. 6. Amethod of ear grinding consisting in rotating the bla n I and a conical helicoidal grinder the pitch helix of which forms in plane development an Archimedean spiral, in a timed relation in such a manner that the ear teeth and thehelicoid while intermeshmg are always tangent to a common rack plane, and in imparting a relative movement of translation to the grinder across the teeth of the blank.

5 7. A method of gear grinding consisting/ that the gear teeth and the helicoid while gent to a common rack plane, and in imparting a relative movement of translation to the grinder in a direction perpendicular to the axis of the blank.

8. A method of gear grinding in which a right helieoidal tapered grinder having less than one full convolution of helix, and having the cone angle, the diameter and the pitch selected with reference to the gear to be generated, is placed in a tangential relation with respect to theimaginary rack plane meshing with said gear at about the middle of its face, in which the grinder and the blank are rotated in a timed relation, in which the grinder is given a relative move ment of translation in a direction transverse to the axis of the blank, and in which,the cutting helicoidal face of the grinder, is periodically trimmed to a correct shape by means of a rapidly rotating trimming element while the, grinder simultaneously slowly rotates and'axially translats in order to.

produce the required lead of helix.

9. A method of gear grinding consisting in rotating the gear blank and .a right helicoidal conical cutter of constant pitch and made of abrasive material, in a timed rela- 'tion to produce the mtermeshing action; in

feeding said cutter relatively across the face of the blank, and in periodically trimming the cutting helicoidal' face of the grinder to cal hobs of a constant conical pitch in a timed relation to a cylindrical gear blank, and in arranging said hobs in such a manner that one side of thegear teetlris generated by one hob and the other side of said teeth is generated-by the other hob during 'the same cutting operation.

'11. A method of hobbing spur gears and the like hich consists in selecting a pair of conical ho s having teeth With opposite sides of difi'erent, radii of curvature, in rotating said hobs timed relation to a gear blank, and in arranging the hobs in such relation to the gear blank that the hob teeth having greater radii of curvature generate the opposite sides of the gear teeth.

In testimony whereof I aflix my signature.

' NIKQLA TRBOJEVICH. 

